Using Evidence-Centered Design to Develop Assessments of Mathematical Knowledge of Teachers for Mathematical Argumentation

• In Event: 21.050 - Developing Measures of Mathematical Knowledge for Teaching for Secondary Teachers: Current Research and Open Questions

Abstract

With the current focus on teaching both mathematical content and mathematical practices, there are new challenges related to both how these practices are taught and also how these practices are assessed. Professional Development (PD) programs are being designed to help teachers develop knowledge and skills to support these practices in classrooms. However, little is known about how to measure teachers’ mathematical knowledge for teaching (MKT) of mathematical practices.
This presentation addresses that gap in the literature. We describe the use of an evidence-centered design (ECD) approach for the development of an assessment of teachers’ MKT for teaching argumentation in middle grades. When assessing teacher knowledge, there are often multiple purposes for an assessment. While some assessments focus on teachers’ understanding of a trajectory of concepts and/or teachers’ understanding of how students engage with these concepts, the assessment discussed here focuses on teachers own knowledge of the mathematical concept. The practice being assessed is the ability to engage in mathematical argumentation.
One of the challenges of developing an assessment of mathematical argumentation is that this practice is not one in which there is a well-defined and agreed upon definition (Cirillo et al., 2015). This makes it challenging to identify what would constitute evidence of teachers’ engagement with argumentation. The use of an ECD approach can help address that challenge (Mislevy & Haertel, 2006) because it requires operationalizing the practice. The first step in this process was to determine the framing of mathematical argumentation that would be used for the assessment. Information was drawn from the curricular materials, professional development materials, and discussions with experts.
From these materials, a set of focal knowledge, skills, and ability statements (FKSAs) that captured the different aspects of mathematical argumentation were developed. For example, one FKSA was “the ability to generate a conjecture based on evidence and/or cases”, while another FKSA was “the ability to generate and/or use a counterexample in a justification.” Once a set of FKSAs was generated and reviewed by experts, tasks were developed that aligned to these FKSAs. One task might contain multiple parts and each part was aligned to one or more FKSAs. These tasks then went through a review and revision process.
The set of tasks was then used as a pre/post test to measure changes in teacher knowledge as the result of participation in PD. Evidence was collected to support the claim that the assessment was able to differentiate between teachers of different abilities. We will discuss further details on the development process and the resulting tasks, and the affordances and limitations of the ECD approach as a tool for developing assessments for mathematical practices.

Authors

• Daisy Wise Rutstein, SRI International

• Hee-Joon Kim, SRI International

• Jennifer Knudsen, SRI International